Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 6 $.
To find $ a_{ 61 } $ we use formula
$$ \color{blue}{a_n = a_1 + (n-1)d}$$In this example we have $ a_1 = 0,~~ d = 6 ~~,~~ n = 61 $. After substituting these values into the formula, we obtain:
$$ \begin{aligned} a_n &= a_1 + d(n-1) \\[1 em] a_{ 61 } &= 0 + (61-1) \cdot 6 \\[1 em] a_{ 61 } &= 0 + 360 \\[1 em] a_{ 61 } &= 360 \end{aligned} $$The first few terms of this sequence are:
$$ 0, ~~~6, ~~~12, ~~~18, ~~~24 . . . $$